/*
 [auto_generated]
 boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp

 [begin_description]
 Implementation of the Runge Kutta Cash Karp 5(4) method. It uses the generic error stepper.
 [end_description]

 Copyright 2009-2011 Karsten Ahnert
 Copyright 2009-2011 Mario Mulansky

 Distributed under the Boost Software License, Version 1.0.
 (See accompanying file LICENSE_1_0.txt or
 copy at http://www.boost.org/LICENSE_1_0.txt)
*/

#ifndef BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED

#include <boost/fusion/container/vector.hpp>
#include <boost/fusion/container/generation/make_vector.hpp>

#include <boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp>
#include <boost/numeric/odeint/algebra/range_algebra.hpp>
#include <boost/numeric/odeint/algebra/default_operations.hpp>

#include <boost/numeric/odeint/util/state_wrapper.hpp>
#include <boost/numeric/odeint/util/is_resizeable.hpp>
#include <boost/numeric/odeint/util/resizer.hpp>

#include <boost/array.hpp>

namespace boost {
namespace numeric {
namespace odeint {

#ifndef DOXYGEN_SKIP
template <class Value = double>
struct rk54_ck_coefficients_a1 : boost::array<Value, 1> {
  rk54_ck_coefficients_a1(void) {
    (*this)[0] = static_cast<Value>(1) / static_cast<Value>(5);
  }
};

template <class Value = double>
struct rk54_ck_coefficients_a2 : boost::array<Value, 2> {
  rk54_ck_coefficients_a2(void) {
    (*this)[0] = static_cast<Value>(3) / static_cast<Value>(40);
    (*this)[1] = static_cast<Value>(9) / static_cast<Value>(40);
  }
};

template <class Value = double>
struct rk54_ck_coefficients_a3 : boost::array<Value, 3> {
  rk54_ck_coefficients_a3(void) {
    (*this)[0] = static_cast<Value>(3) / static_cast<Value>(10);
    (*this)[1] = static_cast<Value>(-9) / static_cast<Value>(10);
    (*this)[2] = static_cast<Value>(6) / static_cast<Value>(5);
  }
};

template <class Value = double>
struct rk54_ck_coefficients_a4 : boost::array<Value, 4> {
  rk54_ck_coefficients_a4(void) {
    (*this)[0] = static_cast<Value>(-11) / static_cast<Value>(54);
    (*this)[1] = static_cast<Value>(5) / static_cast<Value>(2);
    (*this)[2] = static_cast<Value>(-70) / static_cast<Value>(27);
    (*this)[3] = static_cast<Value>(35) / static_cast<Value>(27);
  }
};

template <class Value = double>
struct rk54_ck_coefficients_a5 : boost::array<Value, 5> {
  rk54_ck_coefficients_a5(void) {
    (*this)[0] = static_cast<Value>(1631) / static_cast<Value>(55296);
    (*this)[1] = static_cast<Value>(175) / static_cast<Value>(512);
    (*this)[2] = static_cast<Value>(575) / static_cast<Value>(13824);
    (*this)[3] = static_cast<Value>(44275) / static_cast<Value>(110592);
    (*this)[4] = static_cast<Value>(253) / static_cast<Value>(4096);
  }
};

template <class Value = double>
struct rk54_ck_coefficients_b : boost::array<Value, 6> {
  rk54_ck_coefficients_b(void) {
    (*this)[0] = static_cast<Value>(37) / static_cast<Value>(378);
    (*this)[1] = static_cast<Value>(0);
    (*this)[2] = static_cast<Value>(250) / static_cast<Value>(621);
    (*this)[3] = static_cast<Value>(125) / static_cast<Value>(594);
    (*this)[4] = static_cast<Value>(0);
    (*this)[5] = static_cast<Value>(512) / static_cast<Value>(1771);
  }
};

template <class Value = double>
struct rk54_ck_coefficients_db : boost::array<Value, 6> {
  rk54_ck_coefficients_db(void) {
    (*this)[0] = static_cast<Value>(37) / static_cast<Value>(378) -
        static_cast<Value>(2825) / static_cast<Value>(27648);
    (*this)[1] = static_cast<Value>(0);
    (*this)[2] = static_cast<Value>(250) / static_cast<Value>(621) -
        static_cast<Value>(18575) / static_cast<Value>(48384);
    (*this)[3] = static_cast<Value>(125) / static_cast<Value>(594) -
        static_cast<Value>(13525) / static_cast<Value>(55296);
    (*this)[4] = static_cast<Value>(-277) / static_cast<Value>(14336);
    (*this)[5] = static_cast<Value>(512) / static_cast<Value>(1771) -
        static_cast<Value>(1) / static_cast<Value>(4);
  }
};

template <class Value = double>
struct rk54_ck_coefficients_c : boost::array<Value, 6> {
  rk54_ck_coefficients_c(void) {
    (*this)[0] = static_cast<Value>(0);
    (*this)[1] = static_cast<Value>(1) / static_cast<Value>(5);
    (*this)[2] = static_cast<Value>(3) / static_cast<Value>(10);
    (*this)[3] = static_cast<Value>(3) / static_cast<Value>(5);
    (*this)[4] = static_cast<Value>(1);
    (*this)[5] = static_cast<Value>(7) / static_cast<Value>(8);
  }
};
#endif

template <class State, class Value = double, class Deriv = State, class Time = Value,
          class Algebra = range_algebra, class Operations = default_operations,
          class Resizer = initially_resizer>
#ifndef DOXYGEN_SKIP
class runge_kutta_cash_karp54 : public explicit_error_generic_rk<6, 5, 5, 4, State, Value, Deriv, Time,
                                                                 Algebra, Operations, Resizer>
#else
class runge_kutta_cash_karp54 : public explicit_error_generic_rk
#endif
{

public:
#ifndef DOXYGEN_SKIP
  typedef explicit_error_generic_rk<6, 5, 5, 4, State, Value, Deriv, Time, Algebra, Operations, Resizer>
      stepper_base_type;
#endif
  typedef typename stepper_base_type::state_type state_type;
  typedef typename stepper_base_type::value_type value_type;
  typedef typename stepper_base_type::deriv_type deriv_type;
  typedef typename stepper_base_type::time_type time_type;
  typedef typename stepper_base_type::algebra_type algebra_type;
  typedef typename stepper_base_type::operations_type operations_type;
  typedef typename stepper_base_type::resizer_type resizer_typ;

#ifndef DOXYGEN_SKIP
  typedef typename stepper_base_type::stepper_type stepper_type;
  typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
  typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
#endif

  runge_kutta_cash_karp54(const algebra_type& algebra = algebra_type())
    : stepper_base_type(
          boost::fusion::make_vector(rk54_ck_coefficients_a1<Value>(), rk54_ck_coefficients_a2<Value>(),
                                     rk54_ck_coefficients_a3<Value>(), rk54_ck_coefficients_a4<Value>(),
                                     rk54_ck_coefficients_a5<Value>()),
          rk54_ck_coefficients_b<Value>(), rk54_ck_coefficients_db<Value>(),
          rk54_ck_coefficients_c<Value>(), algebra) {
  }
};

/********** DOXYGEN **********/

/**
 * \class runge_kutta_cash_karp54
 * \brief The Runge-Kutta Cash-Karp method.
 *
 * The Runge-Kutta Cash-Karp method is one of the standard methods for
 * solving ordinary differential equations, see
 * <a
 * href="http://en.wikipedia.org/wiki/Cash%E2%80%93Karp_methods">en.wikipedia.org/wiki/Cash-Karp_methods</a>.
 * The method is explicit and fulfills the Error Stepper concept. Step size control
 * is provided but continuous output is not available for this method.
 *
 * This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current
 * recurring template pattern).
 * Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with
 * error estimation.
 * For more details see explicit_error_stepper_base and explicit_error_generic_rk.
 *
 * \tparam State The state type.
 * \tparam Value The value type.
 * \tparam Deriv The type representing the time derivative of the state.
 * \tparam Time The time representing the independent variable - the time.
 * \tparam Algebra The algebra type.
 * \tparam Operations The operations type.
 * \tparam Resizer The resizer policy type.
 */

/**
 * \fn runge_kutta_cash_karp54::runge_kutta_cash_karp54( const algebra_type &algebra )
 * \brief Constructs the runge_kutta_cash_karp54 class. This constructor can be used as a default
 * constructor if the algebra has a default constructor.
 * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
 */
}
}
}

#endif  // BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
